NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1Question 4
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question. 4
In the formula \(\bar{x}=a+h\,\dfrac{\sum f_i u_i}{\sum f_i}\) for mean of grouped data, \(u_i=\)
(A)
\(\dfrac{x_i+a}{h}\)
(B)
\(h(x_i-a)\)
(C)
\(\dfrac{x_i-a}{h}\)
(D)
\(\dfrac{a-x_i}{h}\)
Detailed Answer with Explanation:
Step 1: The formula given is for the step-deviation method of finding the mean.
Step 2: In this method, \(u_i\) is a new variable that makes calculations easier.
Step 3: We define \(u_i\) as the ratio of the deviation of \(x_i\) from \(a\), divided by the class size \(h\).
Step 4: Mathematically, this means:
\[ u_i = \dfrac{x_i - a}{h} \]
Step 5: Now compare this with the given options. The correct match is option (C): \(\dfrac{x_i - a}{h}\).
Final Answer: Option (C)